This book presents some mathematical methods used in the study of initial and boundary problems for Bingham fluids and rate-depedent viscoplasticity. Existence and uniqueness results are presented and the behaviour of the solution with respect to the data is also studied. For some problems, the numerical approximation of the solution is also given and numerical results are presented. Elliptic variational inequalities, convex functions, monotone operators, semigroups of operators, and nonlinear evolution equations are used as mathematical instruments. The book presents a sudy of some problems of viscoplasticity using various and different mathematical methods, the mathematical results are interpreted from a mathematical point of view, and the theory is developed to deal with numerical results from possible applications in industry and technology.